NEW YORK — Tyson Foods Inc. has won a bidding war to gobble up Hillshire Brands, the maker of Jimmy Dean sausages and Ball Park hot dogs.

Tyson had been vying with rival poultry producer Pilgrim’s Pride to acquire Hillshire, which wrapped up its bidding process Sunday. Tyson’s final offer ended up at $63 per share, about two weeks after Pilgrim’s Pride made an initial bid of $45 per share.

Pilgrim’s Pride, which is owned by Brazilian meat giant JBS, said Monday that it was bowing out of the competition.

Still, the deal is not sealed yet. It is contingent on the termination of Hillshire’s offer to acquire Pinnacle Foods Inc., which makes Birds Eye frozen vegetables and Wish-Bone salad dressings. Pinnacle could choose to cut bait and walk away with $163 million breakup fee, or force the deal to a vote by Hillshire shareholders.

A Pinnacle representative didn’t return a call for comment.

In a conference call with reporters, Tyson CEO Donnie Smith said he was confident the $63 offer would end up being worthwhile for Tyson shareholders, despite how high the price went.

“Great brands like Jimmy Dean and Ball Park just don’t become available very often,” Smith said.

Hillshire’s stock closed at $36.95 on May 9, the day before the company announced the Pinnacle deal. On Monday afternoon after the deal was announced, its shares were up 5 percent at $61.89.

Tyson, like Pilgrim’s Pride, has been looking to boost its presence in brand-name, prepared foods like Jimmy Dean breakfast sandwiches. Those types of products are more profitable than fresh meat, such as chicken breasts, where there isn’t as much wiggle room to pad prices.

While Tyson and Pilgrim’s Pride already sell some brand-name products, their businesses have been more focused on supplying supermarkets and restaurant chains.

In particular, Tyson said it was drawn by Hillshire’s stable of breakfast foods, which would better position it in the fast-growing category.

Tyson also noted the potential for cost savings by combining supply chains, transportation and other operations with Hillshire. But Smith said it was too early to comment on how many jobs could be cut as a result of the deal.

Tyson’s offer will be in place until Dec. 12, the final termination date of the deal with Pinnacle.

Hillshire Brands noted it does not have the right to end the deal with Pinnacle on the basis of the Tyson offer, or enter into an agreement with Tyson before the deal is terminated.

“There can be no assurance that any transaction will result from the Tyson Foods offer,” Hillshire said in a statement.

Hillshire, based in Chicago, had been trying to diversify its own portfolio by moving into other areas of the supermarket with the $4.23 billion acquisition of Pinnacle. But some investors questioned the wisdom of that deal, given the outdated image of many Pinnacle brands and the differences in the two companies’ product portfolios.

The offer from Tyson is worth $7.75 billion based on Hillshire’s 123 million shares outstanding. Tyson values the deal at $8.55 billion, including debt.